I put together a short guide of the creatures that turns up most frequently, partly so that I have something I can refer to, but I also thought it might be of interest to others. I think that it's great that people are actually trying to figure out what they have in their tanks, rather than just go "ew" and nuke it with some poison or other.
Worms
Not a taxonomic group, but treated together here for simplicity. All of them lack any form of shell or legs, although they might have large hairs. If you find a "worm" that doesn't match any of these, check the insect larvae.
Oligochaetes
Clearly segmented worms (when seen close-up), that might be hairy and with or without visible eyes. Size range from miniscule to 10+ cm.
Leeches - Possess suckers at the front and back end, and are most easily identified by their "walking" movements on hard surfaces (similar to inchworms), but can also swim in the free water. Often somewhat dorso-ventrally flattened. Parasitic species are extremely rare in aquaria, instead most are carnivores feeding on snails or other worms. I would be vary of keeping them with snails or shrimp, but all except the smallest of fish should be safe.
Other - Includes a huge number of species, from common live foods such as grindal worms and tubifex, to earthworms and more unusual ones like naidids. Most are detritus feeders living on or in the substrate, although naidids (hairy with eyes and a proboscis) can be free-swimming. Larger or more semi-aquatic species are unlikely to do well at higher temperatures, and might foul the water when they perish, but the group is otherwise only beneficial to have in a tank.
Flatworms
Small unsegmented and flattened worms, often with conspicuous eye spots, and occasionally with the internal organs visible through the skin. Glides across hard surfaces like a snail. Two groups given here:
Planaria - Triangular head with two eye spots. Carnivores feeding on leftover fish food and smaller organisms. Risky with shrimp and snails, but larger fish should be fine.
Rhabdocoela and others - Lacks a distinctive head but might have two eye spots. Harmless detritus feeders, although a population explosion indicates that there is a lot of decomposing matter in the tank (from overfeeding or multiple dead fish for example).
Nematodes
Worms with a rigid cuticle (hard skin) that moves in a jerky fashion. Free-living species rarely encountered in aquaria, but should be mostly harmless.
Pictoral guide to some of the smaller hitchikers, please excuse the horrible look of the
Daphnia (I promise, they do not feed on souls).
Mini-crustaceans
Usually seen as tiny pale specks moving about on the glass, or feebly swimming in the water column. All have a rigid shell, but the exact shape vary greatly. Multiple predatory species exist in the wild (for example the really cool
Leptodora), but all likely to be encountered in aquaria are harmless detritus or algae feeders.
Copepods
Can be divided into multiple groups, including cyclopoids (stocky with short antennae and two egg masses) and calanoids (more slender, with long antennae and one egg mass). Very common in aquaria, and usually move with small jumps across hard surfaces. Detritus feeders, and great live food for tiny fish.
Ostracods
Seed shrimp. The body is encased in a clam-like shell, with only parts of the legs poking out. Seen in aquaria every now and then, especially heavily planted tanks without fish (good water quality indicator). Scuttles around on the bottom or swims low in he water column. Harmless and great live food, but might compete for algae with shrimps.
Cladocerans
Daphnia and company. Larger and more planktonic than the others here, but unlikely to do well in tanks with fish or even weak currents. Harmless feeder on phytoplankton.
Other arthropods
Larger crustaceans
Includes shrimp, caryfish, etc. Two groups given here, with the ones usually encountered being detritus feeders and a good addition to most tanks.
Freshwater isopods (Asellus usually) - Dorso-ventrally flattened, and looks like (and is) an aquatic woodlouse, with the same diet preferences. Good tank janitor, but unlikely to do well at high temperatures.
Amphipods (Gammarus etc) - Laterally flattened and less common than the previous one in freshwater tanks (very common in marine though). Useful part of a cleanup crew, but some wild species are predatory, so be a bit careful if you try to catch your own.
Insects and insect larvae
To many to list all of them here, so I'll settle for some examples and names:
Dipteran (flies and mosquitos) larvae - Worm-like (especially the rat-tailed maggots), but often has at least a hint of legs, antennae and body segments. Feeds on algae and detritus, but are very unlikely to last long in tanks with fish, or to complete their life-cycles indoors.
Caddisfly larvae - The house building ones can be introduced with other wild-caught live foods. Harmless detritus feeders, but unlikely to survive long and unable to reproduce.
Aquatic hemipterans - Includes backswimmers, water boatmen, etc. A mixed bunch, with some predators (backswimmers for example) able to catch fish of their own body size, while others are harmless detrivores. Best not introduced unless you know which one it is.
Dragonfly, dobsonfly and beetle larvae - Underwater "monsters" able to tackle large prey, but a great fun to raise separately from other livestock. Can be confused with mayfly and stonefly larvae, which should be harmless.
Water mites
Tiny round bodies with long legs sticking out. Rarely encountered but should be mostly harmless.